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Stackelberg-Pareto Synthesis ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2024-03-09 Véronique Bruyère, Baptiste Fievet, Jean-François Raskin, Clément Tamines
We study the framework of two-player Stackelberg games played on graphs in which Player 0 announces a strategy and Player 1 responds rationally with a strategy that is an optimal response. While it is usually assumed that Player 1 has a single objective, we consider here the new setting where he has several. In this context, after responding with his strategy, Player 1 gets a payoff in the form of
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First-Order Temporal Logic on Finite Traces: Semantic Properties, Decidable Fragments, and Applications ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2024-03-05 Alessandro Artale, Andrea Mazzullo, Ana Ozaki
Formalisms based on temporal logics interpreted over finite strict linear orders, known in the literature as finite traces, have been used for temporal specification in automated planning, process modelling, (runtime) verification and synthesis of programs, as well as in knowledge representation and reasoning. In this paper, we focus on first-order temporal logic on finite traces. We first investigate
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The Complexity of LTL Rational Synthesis ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2024-02-28 Orna Kupferman, Noam Shenwald
In rational synthesis, we automatically construct a reactive system that satisfies its specification in all rational environments, namely environments that have objectives and act to fulfill them. We complete the study of the complexity of LTL rational synthesis, when the objectives are given by formulas in Linear Temporal Logic. Our contribution is threefold. First, we tighten the known upper bounds
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Characterising Modal Formulas with Examples ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2024-02-27 Balder ten Cate, Raoul Koudijs
We study the existence of finite characterisations for modal formulas. A finite characterisation of a modal formula φ is a finite collection of positive and negative examples that distinguishes φ from every other, non-equivalent modal formula, where an example is a finite pointed Kripke structure. This definition can be restricted to specific frame classes and to fragments of the modal language: a
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An Axiomatic Theory for Reversible Computation ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2024-02-19 Ivan Lanese, Iain Phillips, Irek Ulidowski
Undoing computations of a concurrent system is beneficial in many situations, e.g., in reversible debugging of multi-threaded programs and in recovery from errors due to optimistic execution in parallel discrete event simulation. A number of approaches have been proposed for how to reverse formal models of concurrent computation including process calculi such as CCS, languages like Erlang, and abstract
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Spectrum of FO Logic With Quantifier Depth 4 Is Finite ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2024-01-22 Yury Yarovikov, Maksim Zhukovskii
The k-spectrum is the set of all α > 0 such that G(n, n− α) does not obey the 0-1 law for FO sentences with quantifier depth at most k. In this paper, we prove that the minimum k such that the k-spectrum is infinite equals 5.
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Perspective Games ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2024-01-17 Orna Kupferman, Gal Vardi
We introduce and study perspective games, which model multi-agent systems in which agents can view only the parts of the system that they own. As in standard multi-player turn-based games, the vertices of the game graph are partitioned among the players. Starting from an initial vertex, the players jointly generate a computation, with each player deciding the successor vertex whenever the generated
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Products, Polynomials and Differential Equations in the Stream Calculus ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2024-01-17 Michele Boreale, Luisa Collodi, Daniele Gorla
We study connections among polynomials, differential equations, and streams over a field 𝕂, in terms of algebra and coalgebra. We first introduce the class of (F,G)-products on streams, those where the stream derivative of a product can be expressed as a polynomial function of the streams and their derivatives. Our first result is that, for every (F,G)-product, there is a canonical way to construct
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Algebraic Proof Theory for LE-logics ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2024-01-17 Giuseppe Greco, Peter Jipsen, Fei Liang, Alessandra Palmigiano, Apostolos Tzimoulis
In this article, we extend the research programme in algebraic proof theory from axiomatic extensions of the full Lambek calculus to logics algebraically captured by certain varieties of normal lattice expansions (normal LE-logics). Specifically, we generalize the residuated frames in Reference [34] to arbitrary signatures of normal lattice expansions (LE). Such a generalization provides a valuable
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Decidability of the Satisfiability Problem for Boolean Set Theory with the Unordered Cartesian Product Operator ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2024-01-16 Domenico Cantone, Pietro Ursino
We give a positive solution to the decidability problem for the fragment of set theory, dubbed BST⊗, consisting of quantifier-free formulae involving the Boolean set operators of union, intersection, and set difference, along with the unordered Cartesian product operator ⊗ (where \(s \otimes t := \big \lbrace \lbrace u,v\rbrace \,\texttt {|}\:u \in s \wedge v \in t \big \rbrace\)), and the equality
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On the Complexity of Model Checking Knowledge and Time ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2024-01-16 Laura Bozzelli, Bastien Maubert, Aniello Murano
We establish the precise complexity of the model-checking problem for the main logics of knowledge and time. While this problem was known to be non-elementary for agents with perfect recall, with a number of exponentials that increases with the alternation of knowledge operators, the precise complexity of the problem when the maximum alternation is fixed has been an open problem for 20 years. We close
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Comparing the Expressiveness of the π-calculus and CCS ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-11-18 Rob van Glabbeek
This paper shows that the π-calculus with implicit matching is no more expressive than CCSγ, a variant of CCS in which the result of a synchronisation of two actions is itself an action subject to relabelling or restriction, rather than the silent action τ. This is done by exhibiting a compositional translation from the π-calculus with implicit matching to CCSγ that is valid up to strong barbed bisimilarity
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Extensible Proof Systems for Infinite-State Systems ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-11-18 Rance Cleaveland, Jeroen J. A. Keiren
This article revisits soundness and completeness of proof systems for proving that sets of states in infinite-state labeled transition systems satisfy formulas in the modal mu-calculus in order to develop proof techniques that permit the seamless inclusion of new features in this logic. Our approach relies on novel results in lattice theory, which give constructive characterizations of both greatest
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A Decision Procedure for a Theory of Finite Sets with Finite Integer Intervals ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-11-18 Maximiliano Cristiá, Gianfranco Rossi
In this paper we extend a decision procedure for the Boolean algebra of finite sets with cardinality constraints (ℒ|⋅|) to a decision procedure for ℒ|⋅| extended with set terms denoting finite integer intervals (ℒ[]). In ℒ[] interval limits can be integer linear terms including unbounded variables. These intervals are a useful extension because they allow to express non-trivial set operators such as
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Living without Beth and Craig: Definitions and Interpolants in Description and Modal Logics with Nominals and Role Inclusions ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-10-10 Alessandro Artale, Jean Christoph Jung, Andrea Mazzullo, Ana Ozaki, Frank Wolter
The Craig interpolation property (CIP) states that an interpolant for an implication exists iff it is valid. The projective Beth definability property (PBDP) states that an explicit definition exists iff a formula stating implicit definability is valid. Thus, the CIP and PBDP reduce potentially hard existence problems to entailment in the underlying logic. Description (and modal) logics with nominals
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Inputs, Outputs, and Composition in the Logic of Information Flows ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-08-25 Heba Aamer, Bart Bogaerts, Dimitri Surinx, Eugenia Ternovska, Jan Van den Bussche
The logic of information flows (LIF) is a general framework in which tasks of a procedural nature can be modeled in a declarative, logic-based fashion. The first contribution of this article is to propose semantic and syntactic definitions of inputs and outputs of LIF expressions. We study how the two relate and show that our syntactic definition is optimal in a sense that is made precise. The second
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First-order Logic with Connectivity Operators ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-07-25 Nicole Schirrmacher, Sebastian Siebertz, Alexandre Vigny
First-order logic (FO) can express many algorithmic problems on graphs, such as the independent set and dominating set problem parameterized by solution size. However, FO cannot express the very simple algorithmic question whether two vertices are connected. We enrich FO with connectivity predicates that are tailored to express algorithmic graph problems that are commonly studied in parameterized algorithmics
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Generating Extended Resolution Proofs with a BDD-Based SAT Solver ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-07-25 Randal E. Bryant, Marijn J. H. Heule
In 2006, Biere, Jussila, and Sinz made the key observation that the underlying logic behind algorithms for constructing Reduced, Ordered Binary Decision Diagrams (BDDs) can be encoded as steps in a proof in the extended resolution logical framework. Through this, a BDD-based Boolean satisfiability (SAT) solver can generate a checkable proof of unsatisfiability. Such a proof indicates that the formula
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Local Search For Satisfiability Modulo Integer Arithmetic Theories ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-07-25 Shaowei Cai, Bohan Li, Xindi Zhang
Satisfiability Modulo Theories (SMT) refers to the problem of deciding the satisfiability of a formula with respect to certain background first-order theories. In this article, we focus on Satisfiablity Modulo Integer Arithmetic, which is referred to as SMT(IA), including both linear and non-linear integer arithmetic theories. Dominant approaches to SMT rely on calling a CDCL-based SAT solver, either
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Inputs, Outputs, and Composition in the Logic of Information Flows ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-07-15 Heba Aamer, Bart Bogaerts, Dimitri Surinx, Eugenia Ternovska, Jan Van den Bussche
The logic of information flows (LIF) is a general framework in which tasks of a procedural nature can be modeled in a declarative, logic-based fashion. The first contribution of this paper is to propose semantic and syntactic definitions of inputs and outputs of LIF expressions. We study how the two relate and show that our syntactic definition is optimal in a sense that is made precise. The second
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Interpolation Results for Arrays with Length and MaxDiff ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-06-09 Silvio Ghilardi, Alessandro Gianola, Deepak Kapur, Chiara Naso
In this article, we enrich McCarthy’s theory of extensional arrays with a length and a maxdiff operation. As is well-known, some diff operation (i.e., some kind of difference function showing where two unequal arrays differ) is needed to keep interpolants quantifier free in array theories. Our maxdiff operation returns the max index where two arrays differ; thus, it has a univocally determined semantics
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A Decidable Fragment of First Order Modal Logic: Two Variable Term Modal Logic ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-06-09 Anantha Padmanabha, R. Ramanujam
First order modal logic (𝖥𝖮𝖬𝖫) is built by extending First Order Logic (𝖥𝖮) with modal operators. A typical formula is of the form \(\forall x \exists y \Box P(x,y)\). Not only is 𝖥𝖮𝖬𝖫 undecidable, even simple fragments like that of restriction to unary predicate symbols, guarded fragment and two variable fragment, which are all decidable for 𝖥𝖮 become undecidable for 𝖥𝖮𝖬𝖫. In this
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Living Without Beth and Craig: Definitions and Interpolants in Description and Modal Logics with Nominals and Role Inclusions ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-06-03 Alessandro Artale, Jean Christoph Jung, Andrea Mazzullo, Ana Ozaki, Frank Wolter
The Craig interpolation property (CIP) states that an interpolant for an implication exists iff it is valid. The projective Beth definability property (PBDP) states that an explicit definition exists iff a formula stating implicit definability is valid. Thus, the CIP and PBDP reduce potentially hard existence problems to entailment in the underlying logic. Description (and modal) logics with nominals
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Faster Property Testers in a Variation of the Bounded Degree Model ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-05-10 Isolde Adler, Polly Fahey
Property testing algorithms are highly efficient algorithms that come with probabilistic accuracy guarantees. For a property P, the goal is to distinguish inputs that have P from those that are far from having P with high probability correctly, by querying only a small number of local parts of the input. In property testing on graphs, the distance is measured by the number of edge modifications (additions
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Parameterized Complexity of Logic-based Argumentation in Schaefer’s Framework ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-05-10 Yasir Mahmood, Arne Meier, Johannes Schmidt
Argumentation is a well-established formalism dealing with conflicting information by generating and comparing arguments. It has been playing a major role in AI for decades. In logic-based argumentation, we explore the internal structure of an argument. Informally, a set of formulas is the support for a given claim if it is consistent, subset-minimal, and implies the claim. In such a case, the pair
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Mixed Iterated Revisions: Rationale, Algorithms, and Complexity ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-05-10 Paolo Liberatore
Several forms of iterable belief change exist, differing in the kind of change and its strength: some operators introduce formulae, others remove them; some add formulae unconditionally, others only as additions to the previous beliefs; some only relative to the current situation, others in all possible cases. A sequence of changes may involve several of them: for example, the first step is a revision
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Interval Temporal Logic for Visibly Pushdown Systems ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-04-17 Laura Bozzelli, Angelo Montanari, Adriano Peron
In this article, we introduce and investigate an extension of Halpern and Shoham’s interval temporal logic HS for the specification and verification of branching-time context-free requirements of pushdown systems under a state-based semantics over Kripke structures enforcing visibility of the pushdown operations. The proposed logic, called nested BHS, supports branching-time both in the past and in
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Circular (Yet Sound) Proofs in Propositional Logic ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-04-07 Albert Atserias, Massimo Lauria
Proofs in propositional logic are typically presented as trees of derived formulas or, alternatively, as directed acyclic graphs of derived formulas. This distinction between tree-like vs. dag-like structure is particularly relevant when making quantitative considerations regarding, for example, proof size. Here we analyze a more general type of structural restriction for proofs in rule-based proof
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Reasoning about Quality and Fuzziness of Strategic Behaviors ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-04-07 Patricia Bouyer, Orna Kupferman, Nicolas Markey, Bastien Maubert, Aniello Murano, Giuseppe Perelli
Temporal logics are extensively used for the specification of on-going behaviors of computer systems. Two significant developments in this area are the extension of traditional temporal logics with modalities that enable the specification of on-going strategic behaviors in multi-agent systems, and the transition of temporal logics to a quantitative setting, where different satisfaction values enable
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Eager Equality for Rational Number Arithmetic ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-04-07 Jan A. Bergstra, John V. Tucker
Eager equality for algebraic expressions over partial algebras distinguishes or separates terms only if both have defined values and they are different. We consider arithmetical algebras with division as a partial operator, called meadows, and focus on algebras of rational numbers. To study eager equality, we use common meadows, which are totalisations of partial meadows by means of absorptive elements
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Number of Variables for Graph Differentiation and the Resolution of Graph Isomorphism Formulas ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-04-07 Jacobo Torán, Florian Wörz
We show that the number of variables and the quantifier depth needed to distinguish a pair of graphs by first-order logic sentences exactly match the complexity measures of clause width and depth needed to refute the corresponding graph isomorphism formula in propositional narrow resolution. Using this connection, we obtain upper and lower bounds for refuting graph isomorphism formulas in (normal)
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Semantic Analysis of a Linear Temporal Extension of Quantum Logic and Its Dynamic Aspect ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-03-17 Tsubasa Takagi
Although various dynamic or temporal logics have been proposed to verify quantum protocols and systems, these two viewpoints have not been studied comprehensively enough. We propose Linear Temporal Quantum Logic (LTQL), a linear temporal extension of quantum logic with a quantum implication, and extend it to Dynamic Linear Temporal Quantum Logic (DLTQL). This logic has temporal operators to express
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Hardness Characterisations and Size-width Lower Bounds for QBF Resolution ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-01-27 Olaf Beyersdorff, Joshua Blinkhorn, Meena Mahajan, Tomáš Peitl
We provide a tight characterisation of proof size in resolution for quantified Boolean formulas (QBF) via circuit complexity. Such a characterisation was previously obtained for a hierarchy of QBF Frege systems [16], but leaving open the most important case of QBF resolution. Different from the Frege case, our characterisation uses a new version of decision lists as its circuit model, which is stronger
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Linear Logic Properly Displayed ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-01-28 Giuseppe Greco, Alessandra Palmigiano
We introduce proper display calculi for intuitionistic, bi-intuitionistic and classical linear logics with exponentials, which are sound, complete, conservative, and enjoy cut elimination and subformula property. Based on the same design, we introduce a variant of Lambek calculus with exponentials, aimed at capturing the controlled application of exchange and associativity. Properness (i.e., closure
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Testing using CSP Models: Time, Inputs, and Outputs ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-01-28 James Baxter, Ana Cavalcanti, Maciej Gazda, Robert M. Hierons
The existing testing theories for CSP cater for verification of interaction patterns (traces) and deadlocks, but not time. We address here refinement and testing based on a dialect of CSP, called tock-CSP, which can capture discrete time properties. This version of CSP has been of widespread interest for decades; recently, it has been given a denotational semantics, and model checking has become possible
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Witnesses for Answer Sets of Logic Programs ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-01-27 Yisong Wang, Thomas Eiter, Yuanlin Zhang, Fangzhen Lin
In this article, we consider Answer Set Programming (ASP). It is a declarative problem solving paradigm that can be used to encode a problem as a logic program whose answer sets correspond to the solutions of the problem. It has been widely applied in various domains in AI and beyond. Given that answer sets are supposed to yield solutions to the original problem, the question of “why a set of atoms
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Generalizing Parikh’s Criterion for Relevance-Sensitive Belief Revision ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-01-27 Theofanis Aravanis
Parikh proposed his relevance-sensitive axiom to remedy the weakness of the classical AGM paradigm in addressing relevant change. An insufficiency of Parikh’s criterion, however, is its dependency on the contingent beliefs of a belief set to be revised, since the former only constrains the revision process of splittable theories (i.e., theories that can be divided in mutually disjoint compartments)
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Good-for-Game QPTL: An Alternating Hodges Semantics ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-01-23 Dylan Bellier, Massimo Benerecetti, Dario Della Monica, Fabio Mogavero
An extension of QPTL is considered where functional dependencies among the quantified variables can be restricted in such a way that their current values are independent of the future values of the other variables. This restriction is tightly connected to the notion of behavioral strategies in game-theory and allows the resulting logic to naturally express game-theoretic concepts. Inspired by the work
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Logics for Temporal Information Systems in Rough Set Theory ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-01-20 Md. Aquil Khan, Mohua Banerjee, Sibsankar Panda
The article discusses temporal information systems (TISs) that add the dimension of time to complete or incomplete information systems. Through TISs, one can accommodate the possibility of domains or attribute values for objects changing with time or the availability of currently missing information with time. Different patterns of flow of information give different TISs. The corresponding logics with
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A Decision Procedure for Guarded Separation Logic Complete Entailment Checking for Separation Logic with Inductive Definitions ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-01-18 Christoph Matheja, Jens Pagel, Florian Zuleger
We develop a doubly exponential decision procedure for the satisfiability problem of guarded separation logic—a novel fragment of separation logic featuring user-supplied inductive predicates, Boolean connectives, and separating connectives, including restricted (guarded) versions of negation, magic wand, and septraction. Moreover, we show that dropping the guards for any of the preceding connectives
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Continuous One-counter Automata ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-01-18 Michael Blondin, Tim Leys, Filip Mazowiecki, Philip Offtermatt, Guillermo Pérez
We study the reachability problem for continuous one-counter automata, COCA for short. In such automata, transitions are guarded by upper- and lower-bound tests against the counter value. Additionally, the counter updates associated with taking transitions can be (non-deterministically) scaled down by a nonzero factor between zero and one. Our three main results are as follows: we prove (1) that the
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The Complexity of Quantified Constraints: Collapsibility, Switchability, and the Algebraic Formulation ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-01-18 Catarina Carvalho, Florent Madelaine, Barnaby Martin, Dmitriy Zhuk
Let 𝔸 be an idempotent algebra on a finite domain. By mediating between results of Chen [1] and Zhuk [2], we argue that if 𝔸 satisfies the polynomially generated powers property (PGP) and ℬ is a constraint language invariant under 𝔸 (i.e., in Inv(𝔸)), then QCSP ℬ is in NP. In doing this, we study the special forms of PGP, switchability, and collapsibility, in detail, both algebraically and logically
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Canonisation and Definability for Graphs of Bounded Rank Width ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-01-18 Martin Grohe, Daniel Neuen
We prove that the combinatorial Weisfeiler-Leman algorithm of dimension (3k+4) is a complete isomorphism test for the class of all graphs of rank width at most k. Rank width is a graph invariant that, similarly to tree width, measures the width of a certain style of hierarchical decomposition of graphs; it is equivalent to clique width. It was known that isomorphism of graphs of rank width k is decidable
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SAT-Inspired Eliminations for Superposition ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-01-18 Petar Vukmirović, Jasmin Blanchette, Marijn J. H. Heule
Optimized SAT solvers not only preprocess the clause set, they also transform it during solving as inprocessing. Some preprocessing techniques have been generalized to first-order logic with equality. In this article, we port inprocessing techniques to work with superposition, a leading first-order proof calculus, and we strengthen known preprocessing techniques. Specifically, we look into elimination
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MaxSAT Resolution and Subcube Sums ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-01-18 Yuval Filmus, Meena Mahajan, Gaurav Sood, Marc Vinyals
We study the MaxSAT Resolution (MaxRes) rule in the context of certifying unsatisfiability. We show that it can be exponentially more powerful than tree-like resolution, and when augmented with weakening (the system MaxResW), p-simulates tree-like resolution. In devising a lower bound technique specific to MaxRes (and not merely inheriting lower bounds from Res), we define a new proof system called
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Reducible Theories and Amalgamations of Models ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-01-18 Bahar Aameri, Michael Grüninger
Within knowledge representation in artificial intelligence, a first-order ontology is a theory in first-order logic that axiomatizes the concepts in some domain. Ontology verification is concerned with the relationship between the intended models of an ontology and the models of the axiomatization of the ontology. In particular, we want to characterize the models of an ontology up to isomorphism and
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On monotonic determinacy and rewritability for recursive queries and views ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2023-01-05 Michael Benedikt, Stanislav Kikot, Piotr Ostropolski-Nalewaja, Miguel Romero
A query Q is monotonically determined over a set of views V if Q can be expressed as a monotonic function of the view image. In the case of relational algebra views and queries, monotonic determinacy coincides with rewritability as a union of conjunctive queries, and it is decidable in important special cases, such as for CQ views and queries [11, 30]. We investigate the situation for views and queries
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On Composing Finite Forests with Modal Logics ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2022-12-29 Bartosz Bednarczyk, Stéphane Demri, Raul Fervari, Alessio Mansutti
We study the expressivity and complexity of two modal logics interpreted on finite forests and equipped with standard modalities to reason on submodels. The logic \(\mathsf {ML} (\,\operatorname{\raisebox {-2pt}{\rule {1.2pt}{2.1ex}}}\,) \) extends the modal logic K with the composition operator \(\operatorname{\raisebox {-2pt}{\rule {1.2pt}{2.1ex}}} \) from ambient logic, whereas \(\mathsf {ML} (\mathbin
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Good-for-Game QPTL: An Alternating Hodges Semantics ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2022-10-21 Dylan Bellier, Massimo Benerecetti, Dario Della Monica, Fabio Mogavero
An extension of QPTL is considered where functional dependencies among the quantified variables can be restricted in such a way that their current values are independent of the future values of the other variables. This restriction is tightly connected to the notion of behavioral strategies in game-theory and allows the resulting logic to naturally express game-theoretic concepts. Inspired by the work
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Precise Subtyping for Asynchronous Multiparty Sessions ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2022-10-20 Silvia Ghilezan, Jovanka Pantović, Ivan Prokić, Alceste Scalas, Nobuko Yoshida
Session subtyping is a cornerstone of refinement of communicating processes: a process implementing a session type (i.e., a communication protocol) T can be safely used whenever a process implementing one of its supertypes T′ is expected, in any context, without introducing deadlocks nor other communication errors. As a consequence, whenever T ≤ T′ holds, it is safe to replace an implementation of
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The Temporal Logic of Coalitional Goal Assignments in Concurrent Multiplayer Games ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2022-10-20 Sebastian Enqvist, Valentin Goranko
We introduce and study a natural extension of the Alternating time temporal logic ATL, called Temporal Logic of Coalitional Goal Assignments (TLCGA). It features one new and quite expressive coalitional strategic operator, called the coalitional goal assignment operator ⦉ γ ⦊, where γ is a mapping assigning to each set of players in the game its coalitional goal, formalised by a path formula of the
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Are Two Binary Operators Necessary to Obtain a Finite Axiomatisation of Parallel Composition? ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2022-10-20 Luca Aceto, Valentina Castiglioni, Wan Fokkink, Anna Ingólfsdóttir, Bas Luttik
Bergstra and Klop have shown that bisimilarity has a finite equational axiomatisation over ACP/CCS extended with the binary left and communication merge operators. Moller proved that auxiliary operators are necessary to obtain a finite axiomatisation of bisimilarity over CCS, and Aceto et al. showed that this remains true when Hennessy’s merge is added to that language. These results raise the question
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Syntactic Completeness of Proper Display Calculi ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2022-10-20 Jinsheng Chen, Giuseppe Greco, Alessandra Palmigiano, Apostolos Tzimoulis
A recent strand of research in structural proof theory aims at exploring the notion of analytic calculi (i.e., those calculi that support general and modular proof-strategies for cut elimination) and at identifying classes of logics that can be captured in terms of these calculi. In this context, Wansing introduced the notion of proper display calculi as one possible design framework for proof calculi
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The Intersection of Algorithmically Random Closed Sets and Effective Dimension ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2022-10-20 Adam Case, Christopher P. Porter
In this article, we study several aspects of the intersections of algorithmically random closed sets. First, we answer a question of Cenzer and Weber, showing that the operation of intersecting relatively random closed sets (random with respect to certain underlying measures induced by Bernoulli measures on the space of codes of closed sets), which preserves randomness, can be inverted: a random closed
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A Category Theoretic View of Contextual Types: From Simple Types to Dependent Types ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2022-10-20 Jason Z. S. Hu, Brigitte Pientka, Ulrich Schöpp
We describe the categorical semantics for a simply typed variant and a simplified dependently typed variant of Cocon, a contextual modal type theory where the box modality mediates between the weak function space that is used to represent higher-order abstract syntax (HOAS) trees and the strong function space that describes (recursive) computations about them. What makes Cocon different from standard
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A Subatomic Proof System for Decision Trees ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2022-10-20 Chris Barrett, Alessio Guglielmi
We design a proof system for propositional classical logic that integrates two languages for Boolean functions: standard conjunction-disjunction-negation and binary decision trees. We give two reasons to do so. The first is proof-theoretical naturalness: The system consists of all and only the inference rules generated by the single, simple, linear scheme of the recently introduced subatomic logic
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Unifying Operational Weak Memory Verification: An Axiomatic Approach ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2022-10-20 Simon Doherty, Sadegh Dalvandi, Brijesh Dongol, Heike Wehrheim
In this article, we propose an approach to program verification using an abstract characterisation of weak memory models. Our approach is based on a hierarchical axiom scheme that captures the observational properties of a memory model. In particular, we show that it is possible to prove correctness of a program with respect to a particular axiom scheme, and we show this proof to suffice for any memory
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A Generalized Realizability and Intuitionistic Logic ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2022-09-29 Aleksandr Yu. Konovalov
Let V be a set of number-theoretical functions. We define a notion of V-realizability for predicate formulas in such a way that the indices of functions in V are used for interpreting the implication and the universal quantifier. In this paper we prove that Intuitionistic Predicate Calculus is sound with respect to the semantics of V-realizability if and only if some natural conditions for V hold.
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On Proof Complexity of Resolution over Polynomial Calculus ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2022-07-22 Erfan Khaniki
The proof system Res (PCd,R) is a natural extension of the Resolution proof system that instead of disjunctions of literals operates with disjunctions of degree d multivariate polynomials over a ring R with Boolean variables. Proving super-polynomial lower bounds for the size of Res(PC1,R)-refutations of Conjunctive normal forms (CNFs) is one of the important problems in propositional proof complexity
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Logics for Temporal Information Systems in Rough Set Theory ACM Trans. Comput. Log. (IF 0.5) Pub Date : 2022-07-19 MD. Aquil Khan, Mohua Banerjee, Sibsankar Panda
The article discusses temporal information systems (TISs) that add the dimension of time to complete or incomplete information systems. Through TISs, one can accommodate the possibility of domains or attribute-values for objects changing with time or the availability of currently missing information with time. Different patterns of flow of information give different temporal information systems. The